Logical Reasoning: Sets and Puzzles

Set theory, Venn diagrams and the reasoning puzzles that open the Mathematics 30-2 diploma.

8 questions, free, marked as you go with a worked explanation on every one.

What this covers

A survey of 120 students asked about after-school activities. It found that 68 play a sport, 45 play a musical instrument, and 22 do both. How many of the students surveyed do neither?
Two sets are described as follows: n(A) = 30, n(B) = 25, and n(A ∩ B) = 12. What is n(A ∪ B)?
Which expression represents the set of elements that are in A but NOT in B?
At a school of 200 students, 90 take biology, 80 take chemistry and 70 take physics. Of these, 30 take both biology and chemistry, 25 take both biology and physics, and 20 take both chemistry and physics. Exactly 10 students take all three. How many students take at least one of the three sciences?
A student notices that 3, 5, 7 are all prime and concludes that every odd number greater than 1 is prime. What kind of reasoning is this, and what single value shows it is false?
Which of the following statements are always true for any two sets A and B within a universal set U?
In a 3 by 3 magic square the numbers 1 through 9 are each used exactly once, and every row, every column and both diagonals add to the same total. What is that total?
A standard deck of 52 cards is shuffled and one card is drawn. Let H be the set of hearts and F the set of face cards (jacks, queens and kings). How many cards are in H ∪ F?